# dBi to dBm Calculator

dBi stands for deciBel Isotropic [1]. It is the gain of an antenna relative to that of an ideal isotropic antenna that radiates energy equally in all directions.

dBm [2] is the power relative to one milliwatt. dBm can be directly converted to Watt and vice versa.

Use this calculator to find the maximum output power of a transmitter in dBm from the antenna gain in dBi.

Enter:

• Antenna gain (dBi)
• Cable Loss (dB)
• Effective Isotropic Radiated Power (EIRP)

ðŸ”„ dBm to dBi

## Formula

PTx = EIRP + LC – GAnt

## Background

In the USA, the FCC regulates the use of Spectrum. One of their mandates is to develop policy and rules with respect to spectrum allocation and use, equipment authorization, and unlicensed devices.

As part of this, the FCC develops rules to ensure that wireless devices don’t interfere with each other. An example of this is EIRP limits for white space technologies.

When a wireless device is equipped with a high gain antenna, it can put out more power than it is allowed to and this can impact other radio frequency systems. The EIRP limit specified in dBm can be used in the equation below

PTx = EIRP + LC – GAnt

along with the antenna gain to ensure that the transmit power is below the limit.

## Example Application

The maximum EIRP for a LoRa device operating at 922 MHz in Japan is +27 dBm.

Let’s say the antenna gain is specified to be 2 dBi. Using these numbers and a cable loss of 1 dB, the maximum output power from the transmitter is restricted to +26 dBm.

In the event that the antenna gain is specified to be 10 dBi, the max output power is limited to only +18 dBm.

As the antenna gain increases, the amount of radiated power in a particular direction increases. The antenna beam becomes more focused. For a fixed EIRP, this requires a reduction in the transmitter power to keep within FCC limits.

## Antenna dBi

An antenna’s dBi value is a measure of its gain compared to a an isotropic antenna. Isotropic antennas radiate signal equally in all directions. An antenna with a higher dBi value has more gain than an antenna with a lower dBi value.

Antenna gain can be calculated from Antenna Factor and Frequency.

When choosing an antenna for a particular application, it is important to consider its gain.

A high gain directional antenna can be a good choice for applications where there is a requirement to maximize the signal strength in a specific direction. This is the case when transmitting a radio signal at a specific target. It’s also the case when receiving a signal from a specific direction.

Directional antennas can also make it more difficult to receive signals from other directions, so they are not always the best choice for every application.

ðŸ’¡ Sometimes an antenna gain is specified in dBd (deciBel relative to a dipole). Use this calculator to convert from dBd to dBi.

## Practical Applications

### Cell Booster Antennas

Cell phone boosters like the one shown in the picture below, ship with two antennas.

The antenna on the left is a directional Yagi-Uda antenna which is to be mounted externally on the top of the building and pointing in the direction of the base station. The other antenna is a panel antenna which is mounted indoors.

### TV Antennas

Antennas for TVs are often directional to maximize the power of the received signal from a fixed TV station.

For best performance these antennas should be mounted outdoors on the top of a roof or at the highest possible point on a building.

## References

[1] Antenna Gain on Wikipedia

[2] dBm on Wikipedia